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Reference frames for Bell inequality violation in the presence of superselection rules

Paterek, T and Kurzyński, P and Oi, D K L and Kaszlikowski, D (2011) Reference frames for Bell inequality violation in the presence of superselection rules. New Journal of Physics, 13. ISSN 1367-2630

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Superselection rules (SSRs) constrain the allowed states and operations in quantum theory. They limit preparations and measurements and hence impact our ability to observe non-locality, in particular the violation of Bell inequalities. We show that a reference frame compatible with a particle number SSR does not allow observers to violate a Bell inequality if and only if it is prepared using only local operations and classical communication. In particular, jointly prepared separable reference frames are sufficient for obtaining violations of a Bell inequality. We study the size and non-local properties of such reference frames using superselection-induced variance. These results suggest the need for experimental Bell tests in the presence of superselection.